Jekyll2019-08-22T01:09:55+00:00https://math.virginia.edu/feed.xmlMathematics at the University of VirginiaOfficial website of Department of Mathematics at the University of VirginiaUVA MathMath Department awarded a Research Training Group grant2019-06-30T00:00:00+00:002019-06-30T00:00:00+00:00https://math.virginia.edu/2019/06/RTG<ul>
<li><a href="https://news.virginia.edu/content/major-grant-helps-mathematicians-train-defining-shapes-and-patterns">Announcement in UVA Today</a></li>
<li><a href="https://math.virginia.edu/geomtop/">Geometry and topology group page</a></li>
</ul>
<p>The Topology and Geometry group in the Department of Mathematics is happy to announce that they are the recipient of a five year <b>$2.5 million Research Training Group grant from the National Science Foundation</b>.
The NSF RTG program is aimed at strengthening the nation’s scientific competitiveness by increasing the number of well-prepared U.S. residents who pursue careers in the mathematical sciences. Nationally, roughly 5 RTG grants are awarded each year by the NSF to support efforts to improve research training by involving undergraduate students, graduate students, postdoctoral associates, and faculty members in structured research groups centered on a common research theme.</p>
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<p>Geometric Topology and Algebraic Topology are areas of mathematics in which one is trying to understand aspects of the global shape of objects, with tools for doing this coming from various mathematical disciplines. Most classically, the objects of study are curves, surfaces, and higher dimensional analogues of these - manifolds, but modern topology also studies things like the ‘shape’ of algebraic structures like number systems satisfying an associative law. Symmetries, in the guise of group theory, also play a major role. Applications range from the use of curvature and symmetry in mathematical physics to the use of homology theory in the emerging field of topological data analysis.</p>
<h3 id="the-uva-topology-group">The UVA Topology group</h3>
<p>The University of Virginia has a long and strong legacy of research in topology. The current UVA topology faculty, who will be leading the RTG activities, are as follows.</p>
<ul>
<li><a href="https://math.virginia.edu/people/jeb2md/">Julia Bergner</a> (Professor) studies algebraic and higher categorical structures in- formed by the homotopical methods of algebraic topology.</li>
<li><a href="https://math.virginia.edu/people/tmk5a/">Thomas Koberda</a> (Associate Professor) studies geometric group theory, particu- larly groups arising as symmetries on curves and surfaces.</li>
<li><a href="https://math.virginia.edu/people/vk6e/">Slava Krushkal</a> (Professor) works in low-dimensional and geometric topology, with interests including 3 and 4 dimensional manifolds and quantum topology.</li>
<li><a href="https://math.virginia.edu/people/njk4x/">Nicholas Kuhn</a> (Professor) is an algebraic topologist who studies the interplay between stable, unstable, and chromatic homotopy.</li>
<li><a href="https://math.virginia.edu/people/sm4cw/">Sara Maloni</a> (Assistant Professor) has interests lying at the intersection of geom- etry and low-dimensional topology, studying deformations of geometric structures.</li>
<li><a href="https://math.virginia.edu/people/tmark/">Thomas Mark</a> (Professor) studies the differential and symplectic topology of 3 and 4 dimensional manifolds, and developing tools for their study.</li>
</ul>UVA MathAnnouncement in UVA Today Geometry and topology group page The Topology and Geometry group in the Department of Mathematics is happy to announce that they are the recipient of a five year $2.5 million Research Training Group grant from the National Science Foundation. The NSF RTG program is aimed at strengthening the nation’s scientific competitiveness by increasing the number of well-prepared U.S. residents who pursue careers in the mathematical sciences. Nationally, roughly 5 RTG grants are awarded each year by the NSF to support efforts to improve research training by involving undergraduate students, graduate students, postdoctoral associates, and faculty members in structured research groups centered on a common research theme.Virginia Integrable Probability Summer School2019-05-08T00:00:00+00:002019-05-08T00:00:00+00:00https://math.virginia.edu/2019/05/integrable-probability-school<p>From May 27 to June 8, 2019, Department of Mathematics of University of Virginia organizes a two-week summer school in Integrable Probability. The aim of the school is to educate the participants in recent trends around Integrable Probability - a rapidly developing field at the interface of probability / mathematical physics / statistical physics on the one hand, and representation theory / integrable systems on the other.</p>
<p><a href="http://frg.int-prob.org/vipss2019/schedule/">School website</a></p>
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<p>The school will have 4 mini-courses:</p>
<ul>
<li> <a href="http://www.pdmi.ras.ru/~dchelkak/index_en.html">Dmitry Chelkak</a> (École Normale Supérieure, Paris, France)
<details>
<summary><strong>Planar Ising model: from combinatorics to CFT and s-embeddings</strong></summary>
<div style="padding:10px">In theoretical physics, the critical planar Ising model serves as a toy example, in which many precursors of Conformal Field Theory objects and structures exist and can be studied directly in discrete, before passing to the small mesh size limit. Mathematically, a number of results on convergence and conformal invariance of such limits were established during the last decade, both for correlation functions and for interfaces (domain walls) arising in the model. In this mini-course we plan to discuss
<ul>
<li> discrete fermions and the Kadanoff-Ceva spin-disorder formalism - crucial tools that allow one to analyse the planar Ising model;</li>
<li> streamlined version of the classical computation of the magnetization via orthogonal polynomials; </li>
<li> results on convergence of critical correlation functions (energy densities, spins, ...) in bounded domains to CFT limits;</li>
<li> recent ideas on appropriate embeddings of weighted planar graphs that play the same role for the planar Ising model as Tutte’s barycentric embeddings do for random walks, allowing one to use discrete complex analysis techniques beyond "regular" lattices.</li>
</ul>
</div>
</details>
</li>
<li> <a href="https://people.smp.uq.edu.au/OleWarnaar/">Ole Warnaar</a> (University of Queensland, Brisbane, Australia)
<details>
<summary><strong>Schur functions and Schur processes</strong></summary>
<div style="padding:10px">
Abstract TBA
</div>
</details>
</li>
<li> <a href="https://search.star.titech.ac.jp/titech-ss/pursuer.act?event=outside&key_t2r2Rid=CTT100380272&lang=en">Tomohiro Sasamoto</a> (Tokyo Institute of Technology, Tokyo, Japan)
<details>
<summary><strong>Fluctuations of 1D exclusion processes: exact analysis and hydrodynamic approach</strong></summary>
<div style="padding:10px">
One dimensional exclusion processes are stochastic processes in which many particles perform random walks under exclusion constraint. They have been playing important role in the fields of stochastic interacting systems in probability theory and non-equilibrium statistical mechanics in physics. For the last two decades, fluctuations of the processes have been studied quite intensively, since the seminal work by Johansson[1-1] on totally asymmetric simple exclusion process (TASEP) showing that the current fluctuation of TASEP with step initial condition is described by the GUE Tracy-Widom distribution. There have been a vast accumulation of generalizations and related results, but there are still many intriguing questions and problems to be solved.
<br /><br />
In these lectures, we discuss a few new directions in the studies of fluctuations of exclusion processes. We also stress that such studies provide valuable insight to other methods based on hydrodynamic ideas which can be applied to a wider class of interacting particle systems. In the first lecture we review the basics of the subject. After introducing a few models such as the asymmetric simple exclusion process(ASEP) and the Kardar-Parisi-Zhang (KPZ) equation, we explain how one can study their fluctuations for the case of TASEP[1-2]. In the second lecture, we show that an approach introduced in [2] using Frobenius determinant can be applied to a large class of models in a unified manner. In the third lecture we explain our recent result on a two-species exclusion process and connection to the nonlinear fluctuating hydrodynamics[3]. In the last lecture we will consider an application of the techniques to study the large derivation in the symmetric exclusion process[4-1,2].
<br /><br />
<strong>References</strong>
<ul>
<li>[1-1] K. Johansson, Shape fluctuations and random matrices, Commun. Math. Phys. (2009) 437-476. [arXiv:math/9903134]</li>
<li>[1-2] T. Sasamoto, Fluctuations of the one-dimensional asymmetric exclusion process using random matrix
techniques, J. Stat. Mech. (2007) P07007. [arXiv:0705.2942]</li>
<li>[2] T. Imamura, T. Sasamoto, Fluctuations for stationary q- TASEP, to appear in Prob. Th. Rel. Fields. [arXiv:1701.05991]</li>
<li>[3] Z. Chen, J. de Gier, I. Hiki, T. Sasamoto, Exact confirmation of 1D nonlinear fluctuating hydrodynamics for a two-species exclusion process, Phys. Rev. Lett. 120, 240601 (2018). [arXiv:1803.06829]</li>
<li>[4-1] T. Imamura, K. Mallick, T. Sasamoto, Large deviations of a tracer in the symmetric exclusion process,
Phys. Rev. Lett. 118, 160601 (2017). [arXiv:1701.05991]</li>
<li>[4-2] T. Imamura, K. Mallick, T. Sasamoto, Distribution of a tagged particle position in the one-dimensional symmetric simple exclusion process with two-sided Bernoulli initial condition, arXiv:1810.06131.</li>
</ul>
</div>
</details>
</li>
<li> <a href="http://blogs.unimelb.edu.au/paul-zinn-justin/">Paul Zinn-Justin</a> (University of Melbourne, Melbourne, Australia)
<details>
<summary><strong>Quantum integrability and symmetric polynomials</strong></summary>
<div style="padding:10px">
Abstract TBA
</div>
</details>
</li>
</ul>
<p>Talks are in Clark 107 (<a href="http://frg.int-prob.org/vipss2019/schedule/">schedule</a>)</p>
<p>The summer school is supported by the National Science Foundation Focused Research Group grant (DMS-1664617)</p>
<p><br /></p>
<p>Organizers: <a href="mailto:lenia.petrov@gmail.com"><i class="fa fa-envelope" aria-hidden="true"></i> Leo Petrov</a>,
<a href="mailto:ais6a@virginia.edu"><i class="fa fa-envelope" aria-hidden="true"></i> Axel Saenz</a></p>
<p>Scientific Committee: <a href="http://www.math.lsa.umich.edu/~baik/Welcome.html">Jinho Baik</a>, <a href="http://math.mit.edu/directory/profile.php?pid=1222/">Alexei Borodin</a>, <a href="http://www.math.columbia.edu/~corwin/">Ivan Corwin</a>, <a href="https://www.mccme.ru/~vadicgor/">Vadim Gorin</a>, <a href="https://lpetrov.cc">Leo Petrov</a></p>UVA MathFrom May 27 to June 8, 2019, Department of Mathematics of University of Virginia organizes a two-week summer school in Integrable Probability. The aim of the school is to educate the participants in recent trends around Integrable Probability - a rapidly developing field at the interface of probability / mathematical physics / statistical physics on the one hand, and representation theory / integrable systems on the other. School websiteThesis defense: Jim Phillips2019-04-22T00:00:00+00:002019-04-22T00:00:00+00:00https://math.virginia.edu/2019/04/Phillips-defense<p><strong>Jim Phillips</strong> will defend the Ph.D. thesis on Tuesday, April 23.
The title is</p>
<p>“<em>Reduction and deformation of one-point Galois covers</em>”.</p>
<ul>
<li>Date: Tuesday, April 23</li>
<li>Time: 1:00 pm</li>
<li>Place: Multi-purpose room at the Rotunda</li>
</ul>
<p>Everyone is invited to attend.</p>UVA MathJim Phillips will defend the Ph.D. thesis on Tuesday, April 23. The title is “Reduction and deformation of one-point Galois covers”. Date: Tuesday, April 23 Time: 1:00 pm Place: Multi-purpose room at the Rotunda Everyone is invited to attend.Thesis defense: Matt Gagne2019-04-21T00:00:00+00:002019-04-21T00:00:00+00:00https://math.virginia.edu/2019/04/Gagne-defense<p><strong>Matt Gagne</strong> will defend the Ph.D. thesis on Wednesday, April 24. The title is</p>
<p>“<em>The family index of the odd signature operator with coeffcients in a flat bundle</em>”.</p>
<p><a href="https://math.virginia.edu/img/news_events/MattGagne_DefensePoster.pdf">Poster (PDF)</a></p>
<ul>
<li>Date: Wednesday, April 24</li>
<li>Time: 1:15 pm</li>
<li>Place: Gilmer 166</li>
</ul>
<p>Everyone is invited to attend.</p>UVA MathMatt Gagne will defend the Ph.D. thesis on Wednesday, April 24. The title is “The family index of the odd signature operator with coeffcients in a flat bundle”. Poster (PDF) Date: Wednesday, April 24 Time: 1:15 pm Place: Gilmer 166 Everyone is invited to attend.2019 Mathematics Final Exercises Ceremony2019-04-21T00:00:00+00:002019-04-21T00:00:00+00:00https://math.virginia.edu/2019/04/final-exercises<p>Final Exercises ceremony for the College and Graduate School of Arts & Sciences will be on Saturday, May 18, 2019. All other schools will participate on Sunday, May 19, 2019. The Lawn ceremony will start promptly at 10 a.m., with school and department ceremonies taking place in the afternoon on both days.</p>
<p>The ceremony times and locations for <b>Mathematics</b> are listed below. These times and locations may be different from past years.</p>
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<p><strong>Fair Weather: Pavilion I, Lower Garden</strong><br />
<strong>Ceremony Start Time: 12 p.m.</strong><br />
Reservation Time: 8 a.m. – 5 p.m.<br />
<em>*Finals on the Lawn, fair-weather sites for department graduation ceremonies.</em></p>
<p><strong>Inclement Weather: Gilmer Hall, Room 130</strong><br />
<strong>Ceremony Start Time: 12:30 p.m.</strong><br />
Reservation Time: 12 p.m. – 3 p.m.<br />
<em>*Finals on the Lawn, all department ceremonies inside.</em></p>
<p><strong>Severe Weather: Gilmer Hall, Room 130</strong><br />
<strong>Ceremony Start Time: 12:30 p.m.</strong><br />
Reservation Time: 12 p.m. – 3 p.m.<br />
<em>*Finals in John Paul Jones Arena, all department ceremonies inside.</em></p>UVA MathFinal Exercises ceremony for the College and Graduate School of Arts & Sciences will be on Saturday, May 18, 2019. All other schools will participate on Sunday, May 19, 2019. The Lawn ceremony will start promptly at 10 a.m., with school and department ceremonies taking place in the afternoon on both days. The ceremony times and locations for Mathematics are listed below. These times and locations may be different from past years.GTA Teaching awards2019-04-20T00:00:00+00:002019-04-20T00:00:00+00:00https://math.virginia.edu/2019/04/GTA%20Awards<p>We are pleased to recognize <b>Mark Lewers</b> and <b>Mark Schrecengost</b> for winning the 2019 Mathematics Department Outstanding Graduate Teaching Assistant award, and <b>Jim Phillips</b> for receiving one of ten All-University Graduate Teaching Awards.</p>
<p>Congratulations to Mark, Mark, and Jim; we appreciate all of your hard work!</p>UVA MathWe are pleased to recognize Mark Lewers and Mark Schrecengost for winning the 2019 Mathematics Department Outstanding Graduate Teaching Assistant award, and Jim Phillips for receiving one of ten All-University Graduate Teaching Awards. Congratulations to Mark, Mark, and Jim; we appreciate all of your hard work!Thesis defense: Gabriel Islambouli2019-04-16T00:00:00+00:002019-04-16T00:00:00+00:00https://math.virginia.edu/2019/04/Islambouli-defense<p><strong>Gabriel Islambouli</strong> will defend the Ph.D. thesis on Thursday, April 18.
The title is</p>
<p>“<em>Parallels Between Heegaard Splittings and Trisections of 4-manifolds</em>”.</p>
<ul>
<li>Date: Thursday, April 18</li>
<li>Time: 2:00 pm</li>
<li>Place: Dell Building 2, Room 100</li>
</ul>
<p>Everyone is invited to attend.</p>UVA MathGabriel Islambouli will defend the Ph.D. thesis on Thursday, April 18. The title is “Parallels Between Heegaard Splittings and Trisections of 4-manifolds”. Date: Thursday, April 18 Time: 2:00 pm Place: Dell Building 2, Room 100 Everyone is invited to attend.Thesis defense: Chris Leonard2019-04-14T00:00:00+00:002019-04-14T00:00:00+00:00https://math.virginia.edu/2019/04/Leonard-defense<p><strong>Chris Leonard</strong> will defend the Ph.D. thesis on Wednesday, April 17.
The title is</p>
<p>“<em>Categorification of Tensor Products of Representations for Current Algebras and Quantum Groups</em>”.</p>
<ul>
<li>Date: Wednesday, April 17</li>
<li>Time: 1:30pm-3:30pm</li>
<li>Place: New Cabell 504</li>
</ul>
<p>Everyone is invited to attend.</p>UVA MathChris Leonard will defend the Ph.D. thesis on Wednesday, April 17. The title is “Categorification of Tensor Products of Representations for Current Algebras and Quantum Groups”. Date: Wednesday, April 17 Time: 1:30pm-3:30pm Place: New Cabell 504 Everyone is invited to attend.Undergraduate thesis defense: Ben Keigwin2019-04-13T00:00:00+00:002019-04-13T00:00:00+00:00https://math.virginia.edu/2019/04/Keigwin-defense<p><strong>Ben Keigwin</strong> will defend the undergraduate thesis on Monday, April 22.
The title is</p>
<p>“<em>Elliptic Curves over Arithmetic Fields</em>”.</p>
<ul>
<li>Date: Monday, April 22</li>
<li>Time: 4:45pm</li>
<li>Place: KER 317</li>
</ul>
<p>Everyone is invited to attend.</p>UVA MathBen Keigwin will defend the undergraduate thesis on Monday, April 22. The title is “Elliptic Curves over Arithmetic Fields”. Date: Monday, April 22 Time: 4:45pm Place: KER 317 Everyone is invited to attend.Undergraduate thesis defense: Yichen Ma2019-04-11T00:00:00+00:002019-04-11T00:00:00+00:00https://math.virginia.edu/2019/04/Ma-defense<p><strong>Yichen Ma</strong> will defend the undergraduate thesis on Friday, April 19.
The title is</p>
<p>“<em>Sofic approximations of groups</em>”.</p>
<ul>
<li>Date: Friday, April 19</li>
<li>Time: 11:00am</li>
<li>Place: Ruffner 177</li>
</ul>
<p>Everyone is invited to attend.</p>UVA MathYichen Ma will defend the undergraduate thesis on Friday, April 19. The title is “Sofic approximations of groups”. Date: Friday, April 19 Time: 11:00am Place: Ruffner 177 Everyone is invited to attend.